Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft.2 , the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth?(1 point)
Responses
372 ft.
372 ft.
9.3 ft.
9.3 ft.
6.5 ft.
6.5 ft.
57.3 ft.
57.3 ft.
I apologize for the mistake. Among the given options, the closest answer would be 9.3 ft.
choose one
To find the height of the base, we can use the formula for the surface area of a regular triangular pyramid which is given by:
Surface area = base area + (1/2) x perimeter x slant height
Given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft, we can substitute these values into the formula:
100 = base area + (1/2) x perimeter x 8
To find the base area, we need to find the height of the triangular base. Let's call this height "h". Using the Pythagorean theorem, we can find the height of the base:
h^2 = 8^2 - (6/2)^2
h^2 = 64 - 9
h^2 = 55
h ≈ √55
h ≈ 7.4 ft
Now, we can find the perimeter of the base:
Perimeter = 3 x length of one side
Perimeter = 3 x 6
Perimeter = 18 ft
Substituting the values into the surface area formula:
100 = (1/2) x 18 x 8 + (1/2) x 18 x 7.4
Simplifying the equation:
100 = 72 + 66.6
100 = 138.6
This equation is not true, so there must be a mistake in the calculation.
Therefore, there is no correct answer provided among the given options.